{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fourier inversion methods\n",
    "\n",
    "\n",
    "Here I want to show how the characteristic function can be used to price derivatives.    \n",
    "Sometimes it will be convenient to use this method, because for some stochastic processes the probability density function is not always known, or can have a quite complicated formula, while the characteristic function is frequently available.    \n",
    "For Lévy processes, in particular, the characteristic function is always known, and is given by the Lévy-Kintchkine representation (see **A3**).    \n",
    "\n",
    "I will present some examples in which I'm going to price European call options using the normal, the Merton and the Variance Gamma characteristic functions.  \n",
    "\n",
    "For more information on this topic I suggest to have a look at [1].\n",
    "\n",
    "## Contents\n",
    "   - [Inversion theorem](#sec1)\n",
    "   - [Numerical inversion](#sec2)\n",
    "   - [Option pricing](#sec3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook I will use a lot the **characteristic function** $\\phi_{X}(\\cdot)$ of the random variable $X$, defined by:\n",
    "\n",
    "\\begin{align}\n",
    "\\phi_{X}(u) &= \\mathbb{E} \\bigl[ e^{iuX} \\bigr] \\nonumber \\\\\n",
    "            &= \\int_{\\mathbb{R}} e^{iux} f_X(x) dx.\n",
    "\\end{align}\n",
    "\n",
    "where $f_X$ is the density of $X$.    \n",
    "The characteristic function is nothing but the **Fourier transform** of $f_X$.    \n",
    "Let us review some properties:\n",
    "-  $\\phi_{X}(u)$ always exists. This is because $\\bigl| \\int_{\\mathbb{R}} e^{iux} f_X(x) dx \\bigr| \\leq \\int_{\\mathbb{R}} | e^{iux} f_X(x)| dx < \\infty$.  Recall that $|e^{iux}|=1$ and $\\int_{\\mathbb{R}} |f_X(x)| dx = 1$.\n",
    "-  $\\phi_{X}(0) = 1$.\n",
    "-  $\\phi_{X}(u)^{*} = \\phi_{X}(-u)$, where $*$ means complex conjugate.\n",
    "\n",
    "The density function can be obtained by taking the **inverse Fourier transform**:\n",
    "\n",
    "$$ f_X(x) = \\frac{1}{2\\pi} \\int_{\\mathbb{R}} e^{-iux} \\phi_X(u) du $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1'></a>\n",
    "## Inversion theorem\n",
    "\n",
    "Let us consider the following representation of the cumulative density function:\n",
    "\n",
    "\\begin{align*}\n",
    "F_X(x) &= \\mathbb{P}(X<x) = \\int_{-\\infty}^x f_X(t) dt \\\\\n",
    "       &= \\frac{1}{2} - \\frac{1}{2\\pi} \\int_{\\mathbb{R}} \\frac{e^{-iux} \\phi_X(u)}{iu} du \n",
    "\\end{align*}\n",
    "\n",
    "By taking the derivative of $F_X$, you can check that it gives the expression for $f_X$.\n",
    "\n",
    "But.... How to obtain this formula?\n",
    "\n",
    "I think this is a quite interesting topic, so... I present the proof.    (for more information have a look at [2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Proof - step 1\n",
    "\n",
    "Let us consider the sign function [wiki](https://en.wikipedia.org/wiki/Sign_function),\n",
    "$$ sgn(x) =  \\begin{cases}\n",
    " -1 &=  x<0 \\\\\n",
    " 0  &=  x=0 \\\\\n",
    " 1  &=  x>0.\n",
    "\\end{cases} $$\n",
    "\n",
    "The step function has Fourier transform equal to \n",
    "$$\\mathcal{F}[sgn(x)] = \\frac{2}{iu}$$ \n",
    "(intended as the [Cauchy principal value](https://en.wikipedia.org/wiki/Cauchy_principal_value) ).\n",
    "\n",
    "In order to prove it, let us consider the function\n",
    "\n",
    "$$ g_a(x) =  \\begin{cases}\n",
    " -e^{ax} &=  x<0 \\\\\n",
    " 0  &=  x=0 \\\\\n",
    " e^{-ax}  &=  x>0.\n",
    "\\end{cases} $$\n",
    "\n",
    "with $a>0$. When $a \\to 0$, the function $g_a(x)$ converges to $sgn(x)$.\n",
    "\n",
    "The Fourier transform of $g_a$ can be computed easily by splitting the integral in two (if you are lazy, have a look at the table [here](https://en.wikipedia.org/wiki/Fourier_transform#Square-integrable_functions,_one-dimensional)):\n",
    "\n",
    "\\begin{align*}\n",
    "\\mathcal{F}[g_a(x)] &= \\frac{1}{a+iu} - \\frac{1}{a-iu} \\\\\n",
    "                  &= - \\frac{2iu}{a^2 + u^2}  \n",
    "\\end{align*}\n",
    "\n",
    "We can send $a\\to 0$ and obtain the relation we were looking for.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Proof - step 2\n",
    "\n",
    "The convolution of the density function $f_X$ with the sign function is given by:\n",
    "\n",
    "\\begin{align*}\n",
    "(f_X * sgn)(x) &= \\int_{-\\infty}^{\\infty} f_X(x+t) \\, sgn(t) \\, dt \\\\\n",
    "               &= \\int_{-\\infty}^{0} f_X(x+t) \\, (-1) dt + \\int_{0}^{\\infty} f_X(x+t)\\, (1) dt \\\\\n",
    "               &= - F_X(x) + 1 - F_X(x) \\\\\n",
    "               &= 1 - 2 F_X(x)\n",
    "\\end{align*}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Proof - step 3\n",
    "\n",
    "By the convolution theorem [wiki](https://en.wikipedia.org/wiki/Convolution_theorem) we know that:\n",
    "\n",
    "$$ (f_X * sgn) = \\mathcal{F}^{-1} \\, \\biggl[ \\mathcal{F}[f_X] \\cdot \\mathcal{F}[sgn] \\biggr] $$\n",
    "\n",
    "Therefore we have that \n",
    "\n",
    "\\begin{align*}\n",
    "  (f_X * sgn)(x) &= \\frac{1}{2\\pi} \\int_{\\mathbb{R}} e^{-iux} \\phi_X(u) \\cdot \\frac{2}{iu} \\, du\n",
    "\\end{align*}\n",
    "\n",
    "#### Proof - conclusion\n",
    "\n",
    "We can put together the steps 2 and 3:\n",
    "\n",
    "$$ 1 - 2 F_X(x) = \\frac{1}{2\\pi} \\int_{\\mathbb{R}} e^{-iux} \\phi_X(u) \\cdot \\frac{2}{iu} \\, du $$\n",
    "\n",
    "Rearranging the terms, we can conclude the proof:\n",
    "\n",
    "$$ F_X(x) = \\frac{1}{2} - \\frac{1}{2\\pi} \\int_{\\mathbb{R}} e^{-iux} \\phi_X(u) \\cdot \\frac{1}{iu} \\, du $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gil Pelaez formulas\n",
    "\n",
    "Recall that for a complex number z,\n",
    "\n",
    "$$ Re[z] = \\frac{z+z^*}{2}  \\quad \\quad Im[z] = \\frac{z-z^*}{i2} $$\n",
    "\n",
    "Starting from the inversion formula, **Gil Pelaez** obtained the following expression:\n",
    "\n",
    "\\begin{align*}\n",
    "  F_X(x) &= \\frac{1}{2} - \\frac{1}{2\\pi} \\int_{\\mathbb{R}} e^{-iux} \\phi_X(u) \\cdot \\frac{1}{iu} \\, du \\\\\n",
    "         &= \\frac{1}{2} - \\frac{1}{2\\pi} \\int_{-\\infty}^0 e^{-iux} \\phi_X(u) \\frac{1}{iu} \\, du\n",
    "              + \\frac{1}{2\\pi} \\int_0^{\\infty} e^{-iux} \\phi_X(u) \\frac{1}{iu} \\, du \\\\\n",
    "         &= \\frac{1}{2} - \\frac{1}{2\\pi} \\int_0^{\\infty} \\biggl(-e^{iux} \\phi_X(-u) + e^{-iux} \\phi_X(u) \\biggr) \\frac{1}{iu} \\, du \\\\\n",
    "         &= \\frac{1}{2} - \\frac{1}{\\pi} \\int_0^{\\infty} \\frac{Im[ e^{-iux} \\phi_X(u) ]}{u} du\n",
    "\\end{align*}\n",
    "\n",
    "This formula can also be written as:\n",
    "\n",
    "$$ F_X(x) = \\frac{1}{2} - \\frac{1}{\\pi} \\int_0^{\\infty} Re\\biggl[ \\frac{ e^{-iux} \\phi_X(u)}{iu} \\biggr] du $$\n",
    "\n",
    "We obtain the expression for the density by taking the derivative:\n",
    "\n",
    "$$ f_X(x) = \\frac{1}{\\pi} \\int_0^{\\infty} Re\\biggl[ e^{-iux} \\phi_X(u) \\biggr] du $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pricing formula by Fourier inversion\n",
    "\n",
    "In the notebook **1.1** we found that the pricing formula for a call option with stike K and maturity T is: \n",
    "\n",
    "$$  C(S_t,K,T) = S_t \\tilde{\\mathbb{Q}} ( S_T > K ) - e^{-r(T-t)} K \\, \\mathbb{Q}( S_T >K ) $$\n",
    "\n",
    "where $\\tilde{\\mathbb{Q}}$ is the probability under the stock numeraire and $\\mathbb{Q}$ is the probability under the money market numeraire.\n",
    "\n",
    "#### This formula is model independent! \n",
    "\n",
    "When the stock follows a geometric Brownian motion, this formula corresponds to the Black-Scholes formula.\n",
    "\n",
    "Now let us express $\\tilde{\\mathbb{Q}}$ and $\\mathbb{Q}$ in terms of the characteristic function using the Gil Pelaez formula.    \n",
    "Let us call $k = \\log \\frac{K}{S_t}$ and $S_T = S_t e^{X_T}$\n",
    "- For $\\mathbb{Q}$ we can write: \n",
    "\n",
    "\\begin{align*}\n",
    "\\mathbb{Q}(S_T >K) &= 1 - \\mathbb{Q}(S_T <K) = 1 - \\mathbb{Q}(X_T < k) \\\\\n",
    "                   &= \\frac{1}{2} + \\frac{1}{\\pi} \\int_0^{\\infty} Re\\biggl[ \\frac{ e^{-iuk} \\phi_X(u)}{iu} \\biggr] du\n",
    "\\end{align*}\n",
    "\n",
    "- In the same way, for $\\tilde{\\mathbb{Q}}$, we can write: \n",
    "\n",
    "\\begin{align*}\n",
    "\\tilde{\\mathbb{Q}}(S_T >K) &= \\frac{1}{2} + \\frac{1}{\\pi} \\int_0^{\\infty} Re\\biggl[ \\frac{ e^{-iuk} \\tilde{\\phi}_X(u)}{iu} \\biggr] du \\\\\n",
    "                          &= \\frac{1}{2} + \\frac{1}{\\pi} \\int_0^{\\infty} Re\\biggl[ \\frac{ e^{-iuk} \\phi_X(u-i)}{iu \\, \\phi_X(-i)} \\biggr] du  \n",
    "\\end{align*}\n",
    "\n",
    "where\n",
    "\n",
    "\\begin{align*}\n",
    " \\tilde{\\phi}_X(u) &= \\mathbb{E}^{\\tilde{\\mathbb{Q}}} \\bigl[ e^{iuX_T} \\bigr] = \\mathbb{E}^{\\mathbb{Q}} \\biggl[ \\frac{d\\tilde{\\mathbb{Q}}}{d \\mathbb{Q}} e^{iuX_T} \\biggr] \\\\  \n",
    "                   &= \\mathbb{E}^{\\mathbb{Q}} \\biggl[ \\frac{S_t e^{X_T}}{S_t \\mathbb{E}^\\mathbb{Q}[e^{X_T}]} e^{iuX_T} \\biggr] \\\\\n",
    "                   &= \\mathbb{E}^{\\mathbb{Q}} \\biggl[ \\frac{e^{(iu+1)X_T}}{\\phi_X(-i)} \\biggr] \\\\\n",
    "                   &= \\frac{\\phi_X(u-i)}{\\phi_X(-i)}\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "(see the notebook **1.1** for a discussion about this change of measure)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2'></a>\n",
    "## Numerical inversion\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as ss\n",
    "from scipy.integrate import quad\n",
    "from functools import partial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cf_normal(u, mu=1, sig=2):\n",
    "    return np.exp( 1j * u * mu - 0.5 * u**2 * sig**2 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cf_gamma(u, a=1, b=2):\n",
    "    return (1 - b * u * 1j)**(-a) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cf_poisson(u, lam=1):\n",
    "    return np.exp( lam * (np.exp(1j * u) -1) ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us consider the following characteristic functions:\n",
    "\n",
    "##### Normal:\n",
    "$\\mathcal{N}(\\mu,\\sigma^2)$, $\\sigma>0$.\n",
    "$$ \\phi_N(u) = e^{i\\mu u - \\frac{1}{2}\\sigma^2 u^2} $$\n",
    "##### Gamma (shape-scale parametrization) \n",
    "$\\Gamma(a,b)$, $a,b >0$.\n",
    "$$ \\phi_G(u) = (1-ibu)^{-a} $$\n",
    "##### Poisson\n",
    "$Po(\\lambda)$, $\\lambda>0$.\n",
    "$$ \\phi_P(u) = e^{\\lambda (e^{iu}-1)} $$\n",
    "\n",
    "I want to check if the Gil Pelaez formula works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gil Pelaez formula for the density\n",
    "# right_lim is the right extreme of integration\n",
    "# cf is the characteristic function\n",
    "\n",
    "def Gil_Pelaez_pdf(x, cf, right_lim):               \n",
    "    integrand = lambda u: np.real( np.exp(-u*x*1j) * cf(u) )\n",
    "    return 1/np.pi * quad(integrand, 1e-15, right_lim )[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-8,10,100)\n",
    "\n",
    "plt.plot(x,ss.norm.pdf(x, loc=1, scale=2), label=\"pdf norm\")\n",
    "plt.plot(x,[Gil_Pelaez_pdf(i,cf_normal,np.inf) for i in x], label=\"Fourier inversion\" )\n",
    "plt.title(\"Comparison: pdf - Gil Pelaez inversion\"); plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NLjc31+3Zs8d1dXW56667zl1xxRXOOedeeumlk/dD1dfXu4yMjNNur6amxjnnXEdHhzv//PPd5s2bnXPOTZkyxT388MPOOee++MUvugULFrj6+npXXV3tsrOzT243PT3dVVRUuJaWFjd58mR33333Oeece/DBB90XvvAF55xztbW1rquryznn3I9//GN3zz33DOo9GqzefsfAetePNmKk3wbdRopzzrm3H7jO+18heGu7b6x7c83dfscSOSW1kbHdRva3fezLqY/LgX3OuQMAZvYEcDWwI6wVY3+NzvJ+NtX4GkNEBu4bz25nR0V9WNc5d/IYvv7heaedJy8vj1WrVgHw8Y9/nB/84AdceOGFFBYWMmPGjJPPP/LII6ddj3PuPRcHP//883zlK1+hrq6Oxx57jHPOOYcnn3ySRx55hI6ODg4fPsyOHTtYuHAhAFdddRUACxYsoKGhgbS0NNLS0khOTqaurg6As846i0mTJgEwbdo0Lr744pPLvPTSS4DXnfMNN9zA4cOHaWtrU9f4IsDbT/+Q5cefZ+2kT5A2/2KaKvcTf+CvrDz8Czb/7VwWffB6vyOKnJbaSLWRfTn1MQcoDXlcFnyup5VmttnM/mxmp/8EhENKpvez8eiQb0pEYkvPnpe6H/e3R6YxY8YwevRoDh48CMAll1zCpk2bmD9/Pm1tbRw8eJDvf//7vPjii2zZsoUrrrjiPV3zJiUlARAXF3fyfvfjjo6O98zTc77QeT7/+c9z9913s3XrVn70ox+pe3wZ8Q7t3MD8Td9ie+JCln/635i/6sMs/9gXmXv3rymOy2fyq//E8ZooOv1JZBipjYwcfTmi1ttvxfV4/C4wxTnXYGaXA78HZrxvRWZ3AHcA5Ofn9zNqD6PGej+bage3HhHxzZn26g2VkpIS1q5dy8qVK3n88cdZvXo1s2fP5uDBg+zfv59p06bx+OOP92ld//zP/8xdd93FE088QUZGBs65k41AfX09o0ePJj09naqqKv785z9zwQUXhP31HD9+nJwcb//Zz3/+87CvXySaNDeewP3mVlosifG3/pJA/P/+q5M8ajQdV68h43cfZvOjd7HsH3/nY1KR01MbGR7R3Eb25YhaGZAX8jgXqAidwTlX75xrCN5/Dkgws6yeK3LOPeKcW+acW5adnT2I2EAgAZIzoElH1ESkf+bMmcPPf/5zFi5cSG1tLXfddRfJyck88sgjXHHFFaxevZopU6b0aV133XUXF154IStWrGDhwoWsWrWKoqIiioqKWLRoEUVFRcybN4/bbrvt5Kkk4Xb//fdz3XXXce6555KV9b6vXpERZctP76agq4TyD/w72ZML3jd9+qJVrC/4DMtOvMiG5342/AFFIpzayMhh3jVsp5nBLB7YA3wIKAfeAf7OObc9ZJ6JQJVzzpnZcuC3eEfYTrnyZcuWufXr1w8u/Q+WwOTFcO1PB7ceERk2O3fuZM6cOb5tv7i4mCuvvJJt27b5liHW9fY7NrMNzrllPkWKOmFpI0eg+roakv9tJhuzrmDF539xyvk62ts48N1VZHccJu7zG0jPnDCMKUVOTW1kbOtv+3jGI2rOuQ7gbuB5YCfwpHNuu5ndaWZ3Bme7FthmZpuBHwA3nq5IC5uUTHUmIiIiIgDseukxEq2DjJW3nna++IRE7MoHGMsJdr7wX8MTTkSkn/o04HXwdMbnejy3JuT+fwD/Ed5ofTA6C+pKzzyfiEhQQUGB9hSKxKjk3b+nwiYwc8kFZ5x3xuJz2ffsNLL3PYnruheL69PQsiIxTW1kZInub6WUcTqiJiIiItRWlzO3+V0OTbq0z0VXzcwbmNZ5kP1b3xzidCIi/RflhVrw1MdhOMtSREREItfel39FvHUx4Zyb+7zM7Ituo9UlUPOaTn8UkcgT5YVaFnS2QluD30lERETER2n7nqE4Lo/CuWf1eZn0cdlsTT+fOUefp6VJ/0uISGSJ8kItOOi1Tn8UEREZsarK9jO7dRuH867o97Vmycs/yRga2fbir4YonYjIwMRGodaoQk1E+i4QCLB48eKTt+Li4rCs9/bbb2fHjh0DXn7NmjX84hen7lJ8KF1++eXU1dX5sm2RwTr4yn8TZ47ccz/e72XnrryCCptA8rbHhiCZSPRRG/l+frWRfer1MWKNDg5apyNqItIPo0aNYtOmTWFdZ2dnJz/5yU/6vUwgEDj5+M477zzN3IPX0dFBfHzvX/vPPfdcr8+LRIPMg8+yNzCdGdMX9HvZuECAQ/nXsPLQGioO7mJy4ewhSCgSPdRGvp9fbWTUHlF7t+QYn/ntQe+BCjURGaSWlhY+9alPsWDBAoqKinjppZcAePTRR7n77rtPznfllVfy8ssvA5Camsp9993HihUrWLt2LRdccAHdgxS/8MILrFy5kiVLlnDdddfR0OBd/1JQUMA3v/lNVq9ezW9+85v3ZLj//vv5/ve/D8AFF1zAV77yFZYvX87MmTN57bXXAFixYgXbt28/ucwFF1zAhg0baGxs5LbbbuOss86iqKiIP/zhDyfzX3fddXz4wx/m4osv5vDhw5x33nksXryY+fPnn1xvQUEBR48eBeCBBx5g/vz5zJ8/nwcffBDwBkGdM2cOn/nMZ5g3bx4XX3wxzc3N4fsFiAxQ2b5tzOjYS03hhwe8jsILP0OXM0pefCSMyURih9pIf9rIqC3UkuMDrK0MPmg66msWEYkuzc3NJ0/puOaaawB46KGHANi6dSuPP/44n/zkJ2lpaTntehobG5k/fz5vvfUWq1evPvn80aNH+fa3v81f//pX3n33XZYtW8YDDzxwcnpycjKvv/46N95442nX39HRwdtvv82DDz7IN77xDQBuvPFGnnzySQAOHz5MRUUFS5cu5Tvf+Q4f/OAHeeedd3jppZf48pe/TGNjIwBr167l5z//OX/729947LHHuOSSS9i0aRObN29m8eLF79nmhg0b+NnPfsZbb73FunXr+PGPf8zGjRsB2Lt3L5/73OfYvn07GRkZPPXUU2d8r0WGWvmGPwKQd84NA17HxLzp7ExawISKF8MVSyRqqY2MnDYyak99LMwaTaONotPiCeiImkh0+vO9ULk1vOucuAAu+39PO0tvp3W8/vrrfP7znwdg9uzZTJkyhT179px2PYFAgI997GPve37dunXs2LGDVatWAdDW1sbKlStPTr/hhr79Q/nRj34UgKVLl568RuD666/noosu4hvf+AZPPvkk1113HeDtnXzmmWdO7m1saWmhpKQEgIsuuohx48YBcNZZZ3HbbbfR3t7ORz7ykfc1Qq+//jrXXHMNo0ePPpnhtdde46qrrqKwsPDk/KGZRPwUKH+HasYxuWDWoNZzIu8DzNv/71SV7WdC7rQwpRMZBLWRpzUS2sioPaI2KjFATkYKDXHpOvVRRAbNnWI8xvj4eLq6uk4+Dt2DmJyc/J7z50PXddFFF7Fp0yY2bdrEjh07+K//+t9xmrq/4M8kKSkJ8Bq7jo4OAHJycsjMzGTLli38+te/PrnH0TnHU089dXKbJSUlzJkz533bO++883j11VfJycnhlltued+F2ad6H0Lz9Mwk4qfJJ7ZQljq/37099jRhqXfq5KG3nglHLJGYojby9O9DaJ6emQYjao+oAUwfn0pNWRrp6vVRJDqdYa/ecDrvvPP41a9+xQc/+EH27NlDSUkJs2bNor6+nocffpiuri7Ky8t5++23z7ius88+m8997nPs27eP6dOn09TURFlZGTNnzgxL1htvvJHvfe97HD9+nAULvM4TLrnkEn74wx/ywx/+EDNj48aNFBUVvW/ZQ4cOkZOTw2c+8xkaGxt59913+cQnPvGe9+HWW2/l3nvvxTnH008/zS9/+cuw5BYJtyMVxUx21ZRMumXQ6yqYvZQqMok/8CLw/ww+nMhgqY0ckFhqI6P2iBrAtOxUqjpG43RETUQG6bOf/SydnZ0sWLCAG264gUcffZSkpCRWrVpFYWEhCxYs4Etf+hJLliw547qys7N59NFHuemmm1i4cCFnn302u3btClvWa6+9lieeeILrr7/+5HNf+9rXaG9vZ+HChcyfP5+vfe1rvS778ssvs3jxYoqKinjqqaf4whe+8J7pS5Ys4dZbb2X58uWsWLGC22+/vdfGTCQSlG55GYCxs1affsY+sLg4Do07hxkN62lvax30+kRiidpIz3C3kXa6Q3hDadmyZa6755eBeuytEsb88TNcknWEhC+8G6ZkIjKUdu7cefJ0A4lNvf2OzWyDc26ZT5GiTjjayJFg3X/eSVHlb7GvlpGYlDzo9b37/C9ZsvZutl/8OPPOuTwMCUX6R21kbOtv+xjlR9RGU+PSNOC1iIjICDS2ZiMHEmeGpUgDmHH2FbS7APVb/xyW9YmIDEZUF2rTx6dyjDTi245Dpy5qFxGRoWFml5rZbjPbZ2b39jL9ZjPbEry9aWaLQqYVm9lWM9tkZjpMFiYtzY0Utu+lLit8px2lpY9jT9I8JlS9GrZ1iogMVFQXauNGJ9KckIHhoPmY33FERCQGmVkAeAi4DJgL3GRmc3vMdhA43zm3EPgW0HPk5A845xbr9M/wKd7yBonWSXLhyjPP3A8n8j7A1K5iqssPhnW9IiL9FdWFmpmROGa890AdiohEDb+ujZWhF6O/2+XAPufcAedcG/AEcHXoDM65N51z3XsM1wG5w5xxxKnb8zoA+YsuCOt6u7vpL173h7CuV6SvYvR7dMQbyO81qgs1gLSxE7w7KtREokJycjI1NTVqiGKQc46amhqSk8NzvVAEyQFKQx6XBZ87lU8DoRc5OeAFM9tgZncMQb4RKenwespsEpkTwlsTv7ebfpHhpTYyNg20fYzqcdQAxmVPgmJoPFbF6AK/04jImeTm5lJWVsaRI0f8jiJDIDk5mdzcmDuYZL081+t/UWb2AbxCLbS/+FXOuQozGw/8j5ntcs697yKoYBF3B0B+fv7gU8cw19VFftM2DqSfHfZDl93d9M+p+Svtba0kJCadeSGRMFEbGbsG0j5GfaE2YZK3U/NodQV9G8dcRPyUkJBAYWGh3zFE+qMMyAt5nAtU9JzJzBYCPwEuc86dPM3DOVcR/FltZk/jnUr5vkLNOfcIwWvbli1bpt3pp1FRvJMcjrMvd/mQrD9+5oWkrXuWXZtfY/ZZFw7JNkR6ozZSQkX9qY95OV5lWl9b6XMSERGJUe8AM8ys0MwSgRuBZ0JnMLN84HfALc65PSHPjzaztO77wMXAtmFLHqMqtr4CwPi55w7J+qcUecVZ3c5XhmT9IiJ9EfVH1HKzMmhwo2g5Xu13FBERiUHOuQ4zuxt4HggAP3XObTezO4PT1wD3AZnAw2YG0BHs4XEC8HTwuXjgMefcX3x4GTGlq+QtTrhR5M9aOiTrz5yQy6G4XEYdfmtI1i8i0hdRX6jFB+KoD6TTeeKo31FERCRGOeeeA57r8dyakPu3A7f3stwBYFHP52Vwsuq2UJw8mwXxQ/dvTFVGEbNr/0ZXZydxgcCQbUdE5FSi/tRHgNaEDAIt6vVRREQk1nW0t5HXUULj2J5D2YWXTTmHMTRSvFNjlIuIP2KiUHOjMhnVfpzWjk6/o4iIiMgQKj+wg0TrIDBx3pBuJ2fRhwA4sv2lId2OiMipxEShFp+WTYadoKSmye8oIiIiMoRqDmwEYGzh0J5ROil/hjeeWunaId2OiMipxEShlpIxnkzq2Vfd4HcUERERGUKtFdvpckbujMVDuh2Li6M0bTH5DZtxXV1Dui0Rkd7ERKE2JnMio6yNQ5XqUERERCSWJdXupjxuEskpqUO+rc68lWRzjIrinUO+LRGRnmKiUEsckw1AVdX7xh8VERGRGJLVvJ+jKVOHZVsTFnwAgPLNLw7L9kREQsVEoUZKJgC11SrUREREYlVLcyM5nRW0jp01LNvLn1lEHalwSNepicjwi5FCLQuAhmNVdHY5n8OIiIjIUCjfu5mAORImD22Pj93iAgEOpixk8vGNw7I9EZFQMVKoeUfUUjuPc6im0ecwIiIiMhSOFW8GIGtq0bBts3XycnLdYY5WHBq2bYqIQMwUauMAyLQT7K484XMYERERGQrth3fQ5uKZPM98AzoAACAASURBVHV4jqgBjJvrXad2aNNfh22bIiIQK4VacgbOAoyzE+xSoSYiIhKTUup2UxbIJSExadi2WTh/JU0uiY4DbwzbNkVEIFYKtbg4LGUcU5Kb2VOlQk1ERCQWjW8+QG3q9GHdZkJiEgeTZjGubsuwbldEJDYKNYCUTHKSmnTqo4iISAw6cbyWSRyhPXN4enwMVZ+5mIL2A7Q0NQz7tkVk5IqdQi1tIpM5SnFNIy3tnX6nERERkTAq3/MuAKNyFgz7tpMLV5BgnRRvUzf9IjJ8YqdQmzCf7Ob9mOtkX7X2eImIiMSS+kPeqYfjpw1fj4/d8uafC0DdXhVqIjJ8YqdQm7SIQFcb06xCpz+KiIjEmK6qHTS5JCbmzxj2bWdNnkIlWSRUvjvs2xaRkSt2CrWJ3qkQi+IPsVsdioiIiMSU1Pq9lCVMIS4Q8GX7FanzmHximy/bFpGRqU+Fmpldama7zWyfmd17mvnOMrNOM7s2fBH7KHMGxCdzTkq5jqiJiIjEmEmtB6kb5h4fQ7VNXMIkjnC0stS3DCIyspyxUDOzAPAQcBkwF7jJzOaeYr7vAs+HO2SfBOJhwjzmB0pUqImIiMSQmqoyMjlOV/Yc3zKkz1gJQNnW13zLICIjS1+OqC0H9jnnDjjn2oAngKt7me/zwFNAdRjz9c/EheS37aOyvpnjTe2+xRAREZHwObxvIwCj84a/x8duBfPPod0FaD64zrcMIjKy9KVQywFCj/OXBZ87ycxygGuANeGLNgATF5DUcYJcO6rr1ERERGJEY/kuALIL/SvURo1O41B8AWk1m33LICIjS18KNevlOdfj8YPAV5xzpx3AzMzuMLP1Zrb+yJEjfc3Yd5MWATDXilWoiYiIxAhXs58Wl8D4yYW+5qjJWEBBy246Ozp8zSEiI0NfCrUyIC/kcS5Q0WOeZcATZlYMXAs8bGYf6bki59wjzrllzrll2dnZA4x8GuPn4iyOosRSdlfWh3/9IiIiMuySTxRzODDZtx4fu8XlLSfVmindu8nXHCIyMvSlUHsHmGFmhWaWCNwIPBM6g3Ou0DlX4JwrAH4LfNY59/uwpz2TxBQscwbLEkvZU6lBr0VERGLB2JZS6kblnXnGITZh7ioAqne87nMSERkJzlioOec6gLvxenPcCTzpnNtuZnea2Z1DHbDfJi1khjvIrsp6nOt5hqaIiIhEk86ODiZ1VtIypsDvKOROW0A9o6F8vd9RRGQEiO/LTM6554DnejzXa8chzrlbBx9rECYuJGPrbwi01FJV38rE9GRf44iIiMjAVZXuY7J1EMjybwy1bnGBAMXJs8mq2+p3FBEZAfo04HVUmej1CDU37hA7D+s6NRERkWhWU7oTgNGTZvmcxNOYXcSUzkM0nqjzO4qIxLjYK9SCPT/Os2K2Vxz3OYyIiIgMRtPhPQCML5jrcxJPSuFZBMxxaNtav6OISIyLvUItZRyMyeWs5HK2V+iImoiISDRzNftpcklkTcz3OwoAOcEORer3v+VzEhGJdbFXqAFMXMD8wCEVaiIiIlFu1IliDsdPxuIi41+WrIl5VJJFQpUGvhaRoRUZ33rhNmkhE9pKqa49xvHmdr/TiIiIyACNaynleAR0zR+qYvQcJjTs8DuGiMS4GC3UFhFHFwvsIDt0VE1ERCQqdbS3MbGritYI6Jo/VOv4heS6So7XHvE7iojEsNgs1ApW4+ISuCiwQR2KiIiIRKmq0r0kWCfxEdA1f6jUwhUAlGzTwNciMnRis1BLTsemXsAV8e+wo1yFmoiISDSqORTsmn9yZHTN3y1//jkANBx8x+ckIhLLYrNQA5h7FTlU01y20e8kIiIiMgBNlZHVNX+39HHZlNkkkqvVoYiIDJ3YLdRmXU4Xccw//got7Z1+pxERkShmZpea2W4z22dm9/Yy/WYz2xK8vWlmi/q6rJya1e6n0SWTOT7X7yjvU5U6h0mNu/yOISIxLHYLtdFZHMs+i4vtHXZVnvA7jYiIRCkzCwAPAZcBc4GbzKznIZ6DwPnOuYXAt4BH+rGsnELyiUMcjs+JmK75Q7VPXMxEjnK0stTvKCISoyLvmy+M4uZexYy4ckr36PRHEREZsOXAPufcAedcG/AEcHXoDM65N51zx4IP1wG5fV1WTi2ztSziuubvNmbqcgDKd7zhcxIRiVUxXahlLLkGgMQ9f/I5iYiIRLEcIPSwSVnwuVP5NPDnAS4rQe1trUzsqqItvdDvKL2aMn8lXc5oOrje7ygiEqPi/Q4wlCw9hz0Jc5h+9G9+RxERkehlvTznep3R7AN4hdrqASx7B3AHQH5+fv9TxpjKkj3kWRfx2ZHVNX+30WkZFAdySTm6xe8oIhKjYvqIGkDJhA8xrXM/HUcP+h1FRESiUxkQev5dLlDRcyYzWwj8BLjaOVfTn2UBnHOPOOeWOeeWZWdnhyV4NKst8brmT4uwrvlDHUmbR27zLlxXl99RRCQGxXyh1jn7SgBqNzzlcxIREYlS7wAzzKzQzBKBG4FnQmcws3zgd8Atzrk9/VlWetccoV3zh+qatJhMjlNVfsDvKCISg2K+UCucMZ8dXVOwPX/xO4qIiEQh51wHcDfwPLATeNI5t93M7jSzO4Oz3QdkAg+b2SYzW3+6ZYf9RUQhq93PCTeKsVmT/I5ySunTvQ5FDqtDEREZAjF9jRrA1KzR/Ddzubn2Rehog/hEvyOJiEiUcc49BzzX47k1IfdvB27v67JyZqMaDlEZn8OMCOyav1vB3BW0Pxug5dB64JN+xxGRGBO5335hEh+IoyqjiATXBpW64FdERCQajGstpz4lMrvm75ackkpJ/BRSa7b5HUVEYlDMF2oAgSlnA9BZ/KbPSURERORMOjs6GN91hLa0yO/9smbMXPJbd6tDEREJuxFRqE2bOo3irgk07Xvd7ygiIiJyBkcqDpJonQTGFfgd5Yzc5CLSaaSieLffUUQkxoyIQm1x3lg2uJkkVLwDrtfha0RERCRC1JR6PT6OGj/N5yRnNm7GCgAqd63zOYmIxJoRUagVZKawLTCH5LZaqNnvdxwRERE5jcZqr60elxuZg12Hyp+9lDYXoK10vd9RRCTGjIhCzcxomniW96BUe7xEREQiWVdNMZ3OGB8FhVpScgqH4gtJq1WHIiISXiOiUAOYULiAYy6VDnUoIiIiEtHi60uotiwSEpP8jtIntRnzyG/dow5FRCSsRkyhtih/HOu7ZtJ+cK3fUUREROQ0UpvLqU2M3IGue7LJRYyhifIDO/yOIiIxZOQUankZbOiayaj6A9B41O84IiIicgqZ7YdpTMn1O0afZXZ3KLJbO4NFJHxGTKGWlZrEodELvQcluk5NREQkErU0NZDNMTrTI38MtW75s5fS6hLoKNngdxQRiSEjplADSMpfSisJ6lBEREQkQlWV7gMgIbPQ5yR9l5CYxKGEQtKObfc7iojEkBFVqM2fMp4tXYW0H1SHIiIiIpGortwbQy11YuSPoRbqWMZ8prTupauz0+8oIhIjRlShtigvg/VdswhUbYH2Zr/jiIiISA8tRw4AkJU70+ck/WM5RaRaM2X7t/odRURixIgq1OZPTuddN4u4rnao2OR3HBEREenB1RbT4hLInJjnd5R+yQp2KFK9S5dXiEh4jKhCbVRigJas+d6DKg1MKSIiEmkSG8qoCkzE4qLrX5T8WUW0uAQ6yjf6HUVEYkR0fQuGQd6UaRwjDXd4i99RREREpIf0lnLqkqJnDLVu8QmJFCdMZ0ytdgSLSHiMuEJtcd5YdnTm01quQk1ERCTSZHdW0jI6esZQC3V87DwK2vbS2dHhdxQRiQEjrlBbMiWDHW4K8Ud3Qqe+SEVERCLF8dojjKEJlzHF7ygDEpezhBRrpWzvZr+jiEgMGHGF2rTsVEoSphLf1Qq1+/2OIyIiIkHVJbsASMyOrq75u42fdTYA1bvVoYiIDN6IK9TMjMDkhd6DSnWhKyIiEilOHPYGu06fFJ2FWu6MRTS5JLrKNvgdRURiwIgr1MD7Im1zARpL1DOTiIhIpGg7ehCA7PxZPicZmEB8PMVJM8mo2+53FBGJASOyUFsydQJ7XS5NJRpLTUREJFJY3SGOM5oxGZl+Rxmw+rHzmdK+n/a2Vr+jiEiU61OhZmaXmtluM9tnZvf2Mv1qM9tiZpvMbL2ZrQ5/1PCZPzmd3UwhuWan31FEREQkaFRjGdWB6OuaP1R8/lKSrZ2SXTr9UUQG54yFmpkFgIeAy4C5wE1mNrfHbC8Ci5xzi4HbgJ+EO2g4JcbHcSJjDmkdNdBQ7XccERERAca2VnBi1GS/YwzKpDnnAFCzRx2KiMjg9OWI2nJgn3PugHOuDXgCuDp0Budcg3POBR+OBhwRblTeIgCaS9WFroiIiN+6OjuZ0FVNW2qe31EGZXLBHI4zGleh6+BFZHD6UqjlAKUhj8uCz72HmV1jZruAP+EdVYtoObOXA1C55x2fk4iIiMjRyhISrQMbV+B3lEGxuDhKkmaReVwdiojI4PSlULNennvfETPn3NPOudnAR4Bv9boiszuC17CtP3LkSP+ShtnCGQVUuExaStWhiIiIiN+Olu4GYFT2VJ+TDF5D5gKmdBTT0tzodxQRiWJ9KdTKgNDzEHKBilPN7Jx7FZhmZlm9THvEObfMObcsOzu732HDKS05gdLEqaTW7fI1h4iIiEBj1QEAMnKm+5xk8JKmnEWCdXJo+1t+RxGRKNaXQu0dYIaZFZpZInAj8EzoDGY23cwseH8JkAjUhDtsuLVkzmNSeyntrU1+RxERERnROmoPATA+b4bPSQZv8tyVANTtU6EmIgN3xkLNOdcB3A08D+wEnnTObTezO83szuBsHwO2mdkmvB4ibwjpXCRipU5ZTLx1cXCHutAVERHxU+B4CUfJIHnUaL+jDNqEnKkcJYO4w7q8QkQGLr4vMznnngOe6/HcmpD73wW+G95oQy9/7tnwFlTueZuZRef6HUdERGTESmmuoCZ+Iu+7biIKWVwc5aNmkX1CHYqIyMD1acDrWJWdN4smkmkv3+p3FBERkREto62ShigfQy1UU/Yi8jvLaDxR53cUEYlSI7pQIy6OqpQZZNZvp7Mr4s/UFBERiUmdHR2M7zpCW1qu31HCJqVgKXHmOLRtrd9RRCRKjexCDeiYvIw57gC7Sqv9jiIiIjIiHa08RKJ1Ejd2it9RwiZn7ioA6g+87XMSEYlWI75Qy557HknWwd7Nb/gdRUREZESqLd8HwKjsQp+ThE/WxDwqySKhcqPfUUQkSo34Qi1j5moAWg7o1AQRERE/nBxDbfI0n5OEV0XqXCY17PA7hohEqRFfqJE6nprEHLKObaSto8vvNCIiEoHM7FIz221m+8zs3l6mzzaztWbWamZf6jGt2My2mtkmM1s/fKmjR3tNMQDjc6N/sOtQbROKmOyqqK0u9zuKiEQhFWpAy6RlLGI3m0uP+R1FREQijJkF8MYIvQyYC9xkZnN7zFYL/APw/VOs5gPOucXOuWVDlzR6BepLvTHUUlL9jhJWY6Z7A1+XbnvN5yQiEo1UqAFjZ51LttWzbdtmv6OIiEjkWQ7sc84dcM61AU8AV4fO4Jyrds69A7T7ETDapTSVUxM/0e8YYVew4Bw6XBzN6lBERAZAhRqQMu0cABr3qUMRERF5nxygNORxWfC5vnLAC2a2wczuONVMZnaHma03s/VHjhwZYNToFGtjqHVLSU3nUPwUUo5u8juKiEQhFWoA2XNoCYwms3YjTW0dfqcREZHIYr0815/BN1c555bgnTr5OTM7r7eZnHOPOOeWOeeWZWdnDyRnVIrFMdRC1aTPp6BlF65L18GLSP+oUAOIi6Np/BIW2x7WF+s6NREReY8yIC/kcS5Q0deFnXMVwZ/VwNN4p1JKUCyOofYeOcsYQyNl+7f6nUREoowKtaDU6auYZWWs333Q7ygiIhJZ3gFmmFmhmSUCNwLP9GVBMxttZmnd94GLgW1DljQKxeIYaqGy53gDX1fu0OUVItI/8X4HiBSJhSvhNcfxvWvRzk4REenmnOsws7uB54EA8FPn3HYzuzM4fY2ZTQTWA2OALjP7Il4PkVnA02YGXpv7mHPuL368jkgVq2OodcufWUSjS6arVCMziEj/qFDrlrOULuIYV7uJ403tpKck+J1IREQihHPuOeC5Hs+tCblfiXdKZE/1wKKhTRfdYnUMtW6B+HiKk2Yytk6nPopI/+jUx25JaTSPm81S280b+4/6nUZERGREiNUx1ELVZy6moH0/Lc2NfkcRkSiiQi3EqKnnUBTYzys7+3yNuIiIiAyCN4baBL9jDKnkgmUkWifF29f5HUVEoogKtRBx+WczmhYqd7+Nc/3peVlEREQGIqOtKibHUAuVM98bkaFurwo1Eek7FWqhZlxIZ1wC57a+wvaKer/TiIiIxLSuzk7Gd1XTlpp35pmj2PicQqoZR/zhd/2OIiJRRIVaqFFjaZ96EVcF1vLq7kq/04iIiMS0o5UlwTHU8v2OMuTKR89l4gmNzCAifadCrYfkJTcx3uo4uuV//I4iIiIS02rL9gKxO4ZaqJYJS8h1lRw7ctjvKCISJVSo9TTjYloCqcyr+Qt1TW1+pxEREYlZDcEx1NInx2bX/KHSZ5wDwKEtr/icRESihQq1nhKSOTHtSi6Je4c3d5b4nUZERCRmtdcWAzAhL/YLtcKFq2l3AZr3v+l3FBGJEirUejHu7JtJtRZq3v2931FERERiVuB47I+h1m3U6DQOJkxjzFF1KCIifaNCrReBgtUci8+moOJPdHWpm34REZGhMGoEjKEWqnbcYqa27qa9rdXvKCISBVSo9SYujuqCq1jZtYmd+w/4nUZERCQmjW07HPNjqIVKKDibUdZG8fa3/I4iIlFAhdopjF91C/HWRfXax/2OIiIiEnM6OzoY33WEtrTYHkMtVO7CCwCo2fWav0FEJCqoUDuFsYVFHAwUklPyB7+jiIiIxJwjh4uDY6hN8TvKsJmQO41KskioeMfvKCISBVSonUZZwUeZ2bGH6n268FdERCScusdQSxk/1eckw6s8bQE5J7b6HUNEooAKtdPIPf9W2lyAo6/+2O8oIiIiMaWxaj8AGTkzfE4yvNonn8VEjlJZus/vKCIS4VSonUZhfj5rE84mr/RZ6FAPTSIiIuHSUXuILmeMz53md5RhlTnnPADKt7zsbxARiXgq1M7gyIzrSXMnaNisa9VERETCJf54CUdtLEnJKX5HGVYFc5fT5JJoL17ndxQRiXAq1M5g1sqrKHeZNKz7md9RREREYsbo5nJqEib5HWPYJSQmcTBpFpnHNvkdRUQinAq1M5ifN5bn4z/E+CNroa7E7zgiIiIxYVxbJQ0pOX7H8EV99hIK2/fT1HDc7ygiEsFUqJ2BmVE/5wZw0LbhV37HERERiXrtba1ku6N0jqAx1EKlTFtJvHVxcMsbfkcRkQimQq0Pzl5SxBtd8+jY8Evo6vI7joiISFSrLttHwBxxmQV+R/HFlODA1yf2vO5vEBGJaCrU+uCsgnE8F38hKU3lULLW7zgiIiJR7Vi51zX96PEjq8fHbhlZEzkUl8eoyrf9jiIiEUyFWh8E4oz42ZfR5uLp2PlHv+OIiIhEtabqAwCMzZnucxL/VI5dwrTmbXS0t/kdRUQilAq1Pvrgoqm82TWPtu1/BOf8jiMiIhK1OmuL6XBxjM8p9DuKbwKFq0m1Zg5uf8vvKCISoVSo9dHqGVm8Eb+clIYSOLLb7zgiIiJRK+FEGdVx2cQnJPodxTf5RRcBULP9bz4nEZFIpUKtjxICccTPuRyAtu3P+pxGREQkeqU2lVObOPLGUAs1PqeQMptIUrkGvhaR3vWpUDOzS81st5ntM7N7e5l+s5ltCd7eNLNF4Y/qvw+ctZjNXVNp2KJCTUREZKCyOg7TNGqy3zF8V5G+hKlNm+nq7PQ7iohEoDMWamYWAB4CLgPmAjeZ2dwesx0EznfOLQS+BTwS7qCRYNmUsbyVsJyMY1vgRJXfcURERKJOS1MDWdTRmZ7vdxTfWcFq0mmkeOd6v6OISATqyxG15cA+59wB51wb8ARwdegMzrk3nXPHgg/XAbnhjRkZ4uKMuDlXEIejcat6fxQREemvqlKva/6EzJHbkUi33KILAaje+qLPSUQkEvWlUMsBSkMelwWfO5VPA38eTKhItnLleZS5LI5t/L3fUURERKJOXcVeAFInTPU5if8mTZlFJdkklmmMVhF5v74UatbLc732T29mH8Ar1L5yiul3mNl6M1t/5MiRvqeMIHMnp/N20krGH1kHbY1+xxEREYkqLcEx1DLzZvqcJDKUphdR0LgJ19XldxQRiTB9KdTKgLyQx7lARc+ZzGwh8BPgaudcTW8rcs494pxb5pxblp2dPZC8vjMzbNblJNJGzZa/+B1HREQkqrhjh2h1CWROyDvzzCOAy1/FOOop2bPJ7ygiEmH6Uqi9A8wws0IzSwRuBJ4JncHM8oHfAbc45/aEP2ZkWXLu5Rx3KRxd/7TfUURERKJKYkMpVYHxxAUCfkeJCJMXedepVW7RdWoi8l5nLNSccx3A3cDzwE7gSefcdjO708zuDM52H5AJPGxmm8wsprsvmjI+g43JK5hU9TKuo83vOCIiIlEjrbmCuhE+hlqonKlzOcJY4kvf9DuKiESYPo2j5px7zjk30zk3zTn3neBza5xza4L3b3fOjXXOLQ7elg1l6EgQmHc1Y9wJ9q1/we8oIiIiUSOrs4rm0THZOfSAWFwcJWlF5J3QdWoi8l59KtTk/Yo++DGaXBJH3/6N31FERGSImdmlZrbbzPaZ2b29TJ9tZmvNrNXMvtSfZUeShvpjjOUETmOovUdH/irGU0vZ/q1+RxGRCKJCbYBSU8ewL/1spte8TEOLTn8UEYlVZhYAHgIuA+YCN5nZ3B6z1QL/AHx/AMuOGNUl3mXsCVkF/gaJMDlFlwJQ8W7Mjm4kIgOgQm0QUhdfQ7bVse4V9f4oIhLDlgP7nHMHnHNtwBPA1aEzOOeqnXPvAO39XXYkOR4cQy1t4nSfk0SWnKlzqbDxJB56xe8oIhJBVKgNQuHKa2gnnqZNv/M7ioiIDJ0coDTkcVnwuaFeNua0Vu8DYELBiD2o2CuLi6Ns7AqmN26ko11n6YiIR4XaINioDA5nnk1R4+vsraz3O46IiAwN6+U5F+5lzewOM1tvZuuPHDnS53DRxI4dpI5U0sdF51iqQykw/UOkWTP7Nuqomoh4VKgN0thlHyMv7ggvv6rxT0REYlQZEDo6cy5QEe5lnXOPOOeWOeeWZWfHZiGT0lBCdfxkv2NEpGnLL6PLGce2/Y/fUUQkQqhQG6S0hVfTRRy281laOzr9jiMiIuH3DjDDzArNLBG4EXhmGJaNOZlt5dSPyjvzjCNQRtZE9idMJ+Pw635HEZEIoUJtsEZncnz8cs7vXMdftlX6nUZERMLMOdcB3A08D+wEnnTObTezO83sTgAzm2hmZcA9wL+YWZmZjTnVsv68En+1tbYwoauajvQCv6NErKPjz2F62y4a6o/5HUVEIoAKtTBIX/JRZsSV8/IrOv1RRCQWOeeec87NdM5Nc859J/jcGufcmuD9SudcrnNujHMuI3i//lTLjkRVpXsJmCOQNc3vKBErbd5FJFgn+95Wb9IiokItLOIWXkd7IIULjj7OptI6v+OIiIhEnNrSXQCkTZrhc5LINWPph2hySbTu/qvfUUQkAqhQC4eUcbiln+LKuLX88eU3/E4jIiIScZorvTHUsqbM8TlJ5EpKTmHfqIVMrFnndxQRiQAq1MIkcfXncXHxTNvzX1SfaPE7joiISGQ5dpBGl0zm+BE7jFyfNOWdy5SuMqrK9vsdRUR8pkItXMZMomnujXw07hX+8OoGv9OIiIhElFEnDlEZPxmL078epzNh8aUAHHrnTz4nERG/6dsyjMZ86B4SrIuk9Wto6+jyO46IiEjEGNtaxvHkXL9jRLyCOWdxlAwC+9VBmchIp0ItnMZN5ciUK/lo1wv8z4adfqcRERGJCJ0dHUzsrKJ1TIHfUSKexcVxYOwqZjS8TXtbq99xRMRHKtTCLPvSr5BqLdS99EOcc37HERER8V11+X4SrYNA1lS/o0SFhDmXM4Ymdr/9vN9RRMRHKtTCLG7SfEonXsRHm5/irXc3+h1HRETEdzUlXtf8KROn+5wkOsw658O0ugQatuo6NZGRTIXaEJhw3QM4iyPhha+AjqqJiMgI11i5D4CsfHXN3xcpqensGrWY3OpXcF265l1kpFKhNgQSM/PZOuNzLG19m32vPOZ3HBEREV+5mv20ugTGTy70O0rUaCm8iFx3mJK9W/yOIiI+UaE2RBZ87J/YRQGZr30NWur9jiMiIuKbpBOHqAxMJC4Q8DtK1Jiy8qMAHH77dz4nERG/qFAbIinJyWxZfD/pHbXU/PHrfscRERHxTUZzGcfUNX+/TMyfwf5AIWNK/+Z3FBHxiQq1IXTJJVfyay5i7LZHoWqH33FERESGnevqYkLnYVrSpvgdJepUT7yAma3bOV5T5XcUEfGBCrUhlD4qgaplX6LRJdHwwrf9jiMiIjLsaipLSbFWbJy65u+vcUVXEW9d7H3jab+jiIgPVKgNsY9/YDG/4jJS9/8JKrf5HUdERGRYVZfsBGDUBHXN318zis6nhnRsr8ZTExmJVKgNsazUJDpXfJZ6N4rjf9FRNRERGVkaDu8FIDN/ts9Jok9cIMD+jFXMOLGO9rZWv+OIyDBToTYMbvngYh6zK0kv/jMcVje7IiIycnQe3U+7CzAhb4bfUaJS4rwPM4Ymdr75R7+jiMgwU6E2DMYkJ5C0+m7qXQrHnvum33H+//buPD6uut7/+Ot7Zs9kkrRpm7RNt3ShLWBLW9oisokoFBS4LvS6AMrjh+wI6hX1hZP0sQAAIABJREFUPnzch/d6QRRcfnJFFhX9IchOkaogKgiXQhe6t5S2dE/aJmn2TCYz5/v7Y6Y1hKRN20zOTPJ+Ph7zmJmzzHnnm5PzzedsIyIi0m+CjdvY6wzHHwh6HSUvTf3QxTTZCPGVT3gdRUT6mQq1frLwzJN5xPdxhux8EbvnLa/jiIiI9Ivi1h3UhXRr/mMVjkTZWHIGU+tfJtEe9zqOiPQjFWr9JBL0UXLOTdTbKDXP61o1EREZ+NxUilHJXbQW60YixyM445MU0cKG157xOoqI9CMVav3o0tOm82zwQobv/gvJvRu9jiMiIpJV1Ts3U2DacUboRiLHY9rpl9BIlMSqp7yOIiL9SIVaPwr6HSrOv4W4DfDuoju8jiMiIpJV+7euAqCo4kSPk+S3YCjMxpKzmFr/Cu3xVq/jiEg/UaHWzz48axr/KDyfcbufo37vDq/jiIiIZE3bnnUAjJw0w+Mk+S8845PETBsb/qHTH0UGCxVq/cwYw8SLb8NnU6x5UkfVRERk4HJqNlFDCcWlZV5HyXvTTv849RSSXPOk11FEpJ+oUPNA5ZSTWD/kw8zc+xSbtu/yOo6IiEhWFDdvoTo03usYA0IgGGLTkLOZ1vAq8dZmr+OISD9QoeaR8Z/4JjHTxrIn7sZa63UcERGRPmVdl9EdO2iJTfQ6yoAROeVTRE2c9f942usoItIPVKh5JFZ5KlWl8zm38UmeW/6u13FERET61P6q7RSaNhh+gtdRBoxpp11IHUWw+vdeRxGRfqBCzUMjLvw2Zaae6uf/m7qWhNdxRERE+szeLSsBKKw4yeMkA4c/EGRT2YWc1Py/1O3b7XUcEckyFWoe8lWeSePkS7nSfYr7nlzsdRwREZE+07IrfcfHct3xsU+VnXUVQZNi04sPeh1FRLJMhZrHii7+AalAIedu/h5/31jtdRwREZE+YWre5gAxhg4f5XWUAWXC9FPZ5J9C+ZbHsa7rdRwRySIVal4rHI7/gu9xqrOJN574MS3tSa8TiYiIHLeipi1UBcZhHP2r0dcOnLCQ8e4O3ln5itdRRCSLerX1NMacb4x52xiz2RhzWzfjpxpjXjfGtBtjvtb3MQe2wKzP01h+Gtd2PMQ9z73qdRwREZHjYl2XkR3baYpVeh1lQJp23pW02SAHXvul11FEJIuOWKgZY3zAPcAFwHTgX40x07tMVgfcBPywzxMOBsZQ9KmfUeAkOX3Vt3h53U6vE4mIiByzuv17KKEZO0x3fMyGopJS1pacw/SaF2hrafI6johkSW+OqM0FNltrt1prE8CjwMWdJ7DW7rPWLgU6spBxcBg2CfeiH3Oabz2+Jy6npr7R60QiIiLHpHrzKgCiFSd6nGTgKph3JTHTxtq//NbrKCKSJb0p1EYDnQ/x7MoMO2rGmKuNMcuMMcv2799/LB8xoAVnf459Z97Oh+wKdty3EJvULftFRCT/NO9aC0DZxJkeJxm4ps8/n12mnIJ1j3gdRUSypDeFmulmmD2WhVlr77PWzrHWzhk+fPixfMSAV/7ha1lywjeY1foa2x/4PLgpryOJiAx6vbhW2xhjfpoZv9oYM6vTuG3GmDXGmJXGmGX9m9wj+zfSZCMMHznO6yQDlnEcdo37JCcmVrP97ZVexxGRLOhNobYLGNPpfQWwJztxBGDewm/ySMnVjK/+M7VPf93rOCIig1ovr9W+AJiceVwN/LzL+HOstTOttXOynTcXFDZuYU9grO74mGWTL7iOdhug+oW7vY4iIlnQmy3oUmCyMWaCMSYILAQWZTfW4GaM4dyr/pNHnAspXfMgba/d63UkEZHB7IjXamfe/8amLQFKjDEj+ztorihLbKehcKLXMQa80rIKVg39GB+o+SP1NfouVpGB5oiFmrU2CdwA/BnYADxmrV1njLnGGHMNgDGm3BizC7gV+HdjzC5jTFE2gw90I2JhpnzhJ7zkziL04jdx3/6z15FERAar3lyrfbhpLPCCMWa5MebqrKXMEQ21exlGPe6wKV5HGRRGfPQWIibBxj/81OsoItLHenVOgrV2sbV2irV2orX2e5lh91pr7828rrbWVlhri6y1JZnXum3hcZo9YTjVH7mH9e5Yko9dCdVrvI4kIjIY9eZa7cNNc7q1dhbp0yOvN8ac2e1CBsgNt/ZsTl8vFRk1zeMkg8P4aXNYHZ7NxG2/I9Ee9zqOiPQhnTye4z57xjQen3IXtckwrQ9/ARKtXkcSERlsenOtdo/TWGsPPu8DniZ9KuX7DJQbbjVsWQrAyBPmeZxkEJl/PcM5wKo/6QuwRQYSFWo5zhjDbZ85h5/GvkpB07vULvp3ryOJiAw2vblWexFweebuj/OBBmttlTEmaoyJARhjosBHgbX9Gb6/+avfYh9DGTF6gtdRBo2Tz7yUbc4Yhqx+AOu6XscRkT6iQi0PRII+bvo/V/GYs4DStQ9St/YvXkcSERk0enOtNrAY2ApsBu4HrssMLwNeNcasAt4EnrfW/qlff4B+Vta0nt0FU72OMagYx2Hf9C8xKbWF9UsG9OolMqj4vQ4gvTOyOMLJV/6YbQ++ReSpa2ke+waFRUO9jiUiMihYaxeTLsY6D7u302sLXN/NfFuBGVkPmCMaDtQwxu5h14iuN8WUbPvAgqupW/sj3Jd/AB9c4HUcEekDOqKWR6aNLaPuYz9lWGo/y39xLR0pnd4gIiK5Y+fa1wAonNDtZXiSReGCQjZNuoqT21foqJrIAKFCLc/M+uBHeXvSVZzV8id+d//3SbldbzwmIiLijaatbwIw9qTTPU4yOM249KvsZwj89b90rZrIAKBCLQ9N/+wd7C6Zw8KqH/I/v3kYV8WaiIjkgNC+Vewy5RSXlnkdZVCKRGNsnfplpifWsPbV57yOIyLHSYVaPvIFGH3147RFyln47je564m/kL48QkRExDujWjawt3C61zEGtZmX3Ew1wwi+8t86qiaS51So5auCoRR/6Uli/hQXrv0qtz+zTEfWRETEMzXVOyinho7ymV5HGdRC4QJ2nHwDJyQ3svrvj3kdR0SOgwq1PGZGTCW08CGmOju54K1ruPN3i3XNmoiIeGJX5kYiRRP1RddeO+Xj17HblBF97U7cVMrrOCJyjFSo5Tkz+TzMp3/FtMBebnznizx673dJdGijLCIi/Su+bSkpaxh/0mleRxn0AsEQVafcyqTUFpY/+zOv44jIMVKhNgCYEy8hfNMS6ofO4HP77mb9XRfQWrPT61giIjKIFNSsZodvHAWFxV5HEWD2RVezIXAik1b/kIbavV7HEZFjoEJtoCiuYPSNf2bFtG8wtW0F7j3zqH/tQdBNRkREJMus6zImvpH9RbqRSK4wjkPo4h8Rs81s/N2/eR1HRI6BCrWBxHGYddm3WPnxxWxwx1Ly4q00338h1OvomoiIZE/V9k0MoQk7apbXUaSTypPmsazs05xa8yzvvPWK13FE5CipUBuA5s+ZS+GX/8Sd/i/D7hXE7/0w7H/b61giIjJAVW1I30hk6JT5HieRrqZ/9nbqTDH2+a+SSia9jiMiR0GF2gA1bVQJV978Xb459C4a2xK0/uKjJHev8jqWiIgMQB07lpOwfsZNO9XrKNJFUUkp22Z9kynJTSx78i6v44jIUVChNoCNiIX54fULeXj6zznQ4SP+wALqNr7qdSwRERlgimtXsi1QSTAU9jqKdGP2RVezJnQKJ6+/ix2bVnodR0R6SYXaABfy+7jlsgWs/ejvqXULCT/6SVa+/LTXsUREZIBorK9lcmIDtSN0W/5cZRyHsst/RcIEaP/9VSTa415HEpFeUKE2SHzs9FPpuGIx1U450/96FY/++qe0JnSuuoiIHJ/Nry/Cb1xKZlzodRQ5jBGjJ7D1tDuYnNrM8oe+7nUcEekFFWqDyKTKiYy65W9Ux07iM+9+h1/c9W1W7DjgdSwREcljybdfoJEok2ed43UUOYJZH/sCbw65iHm7f8u61573Oo6IHIEKtUEmHBvK2Jv+RH3FOdzSfi8b7r+KHzzxN5riHV5HExGRPOOmUlTW/y/vxObiDwS9jiO9cOKX7mG3M5JhL95ITbW+vkckl6lQG4yCBQz90mMk5nyZhb6/c+OaT/PcnVfy12VrsfqCbBER6aWta19nGPW4E8/zOor0UjRWQvsl91Nkm6h94FPEW5u9jiQiPVChNlj5AgQvuhPfTctpmXIxl7mLOf25s1n2/QvZ/er/g0SL1wlFRCTH7V/xHACVp13scRI5GpNmfIiNH/whJyQ3su7nX8C6rteRRKQbKtQGu6ETKP3cg7jXvcGWsZ9iXHw9o/9yPYk7Kml79lZorfM6oYiI5Kghu19mk38KpWUVXkeRo3TKx67g9Qk3MLvpryz51b95HUdEuqFCTQAIjJjC9KvuJfi1Dfxq8j080zGf4Ipf0nbXDFr/cQ+kdA2biIj804H9VUzp2EjtyLO8jiLHaP4X/pOlJRdw2s77WfrMz7yOIyJdqFCT9ygpjPDFz32e2Tc9zPcnPMjyxBgKXvoWtXedStOWN7yOJyIiOWLLkkU4xlJ6ykVeR5FjZByHGdf+mjWhU5j91r+rWBPJMSrUpFsThxfyrSs/ybDr/sg9Zd+lvaWByG/O5+X7vkpVXaPX8URExGvvvEAdRUyacYbXSeQ4BENhJt30HOvCM9PF2lM/8TqSiGSoUJPDmjqymOuvvZnmL73CyuJzOWvPA+z78dnc/etHeWvHAd0lUkRkEEolk0xsfIMtxfNxfD6v48hxikRjTL75D6yNzOLU1d/hjcfv8jqSiKBCTXppyrgxzLn1CWouuI/Jgf3cuu3LmAfO5cd3fZcn3thMayLpdUQREeknby99kSE0YSbrtvwDRbigkCk3P8eq8KnMW/ddXr/vJtxUyutYIoOaCjU5KsPmXUbB19fSft7tTIi53NJ8Nxcs/iCbvjefpT/5LDsX/wC7+y3QkTYRkQEr/uo9NBBl2lmf8TqK9KFwJMq0W/7AG0M/wWl7HmL1DxfQ1KC7P4t4RYWaHL1wMaHTr6P4a29hL3+WpqmXURgtZGLdK4x5878w959N0+1TqH/8RtjyNxVtIiIDyK7Na5nZ/CrrR3+aaKzE6zjSx4KhMHNveIg3pn2Lk1rfpO4nZ7Jj00qvY4kMSn6vA0geMwZTeTbllWcD0NyeZNHS1VSteJ5x+1/mjLW/h3W/oTo6lfjp/8a4+ZdiHO0bEBHJZ7v/dBcj8DH5wlu9jiJZYhyHeZd9g7WvTWf0i9cSfvg8lpxwM3Mv+6auSRTpR8arm0HMmTPHLlu2zJNlS/btb2rnz6u20bT0ERbUP8w4s48NZiJrxnyO0tmXMm/qWApD2k8gMlgYY5Zba+d4nSNf5GofeWB/FeGffYA1Qz7C3K884nUc6Qf792xjz2+vZkbbG6wPnkzxwvsZXTnN61giA8bh+kcVapJ1dY0tbHnpl4xb9z+MSO6hxYZ4wc5lc+mHGT1+CtMmT+bESZUEgwGvo4pIlqhQOzq52ke+/qtvcNr2e9l22UuMn6Zf52BhXZelz/6MaSv/Gz8pVo75PCd/5jsUFg3xOppI3lOhJrnBdel49zVqX/8tJe8+TzjVfGhUyhrq/aXEC0bjHzqO4rHTCZ/0CRgxHYzxMLSI9AUVakcnF/vIeFsLrd+fys7IVGZ840Wv44gHqnduZvdjX2d201+ppZjN029k9qU34w8EvY4mkrcO1z/q3DPpP45DYOIZlE88AzriUL2altrdbNu+lZqqHXTU7STaUMXohtcJbHsO/nEHe4Njqaq4gMDJlzJ+2hyiYR11ExHxwurnf8FcGtnzoZu8jiIeKR8zifKvPs2mFX8n+cdvM2/9f1G9/hdsm3w5J150A7HioV5HFBlQdERNckpze5KVO+rZsHkLkc1/YGrdS8xy1+MYy7tuGUtCp7NvxOkMLR/LqFEVTKgYzdhhMfw+3aREJJfpiNrRybU+cu+uLfge+DAHfMOY9O2lujGUYF2X1X9/DP+Sn3FiYg1NNsK68ksoO+sqJkw/1et4InlDpz5K3rLWsq9qB3XLnyGy5Y+MqX8TH//8Ak7XGpL4cI0DxqHDX0hTyVTcshlEx8+i+IQzcWIjPPwJRARUqB2tXOoj21qa2H33WZQn91C78HnGTZvtdSTJMZtWvEzT337EBxpfIWBSbPZNpKbyEsaf+VnKx0zyOp5ITlOhJgNH2wHY8xbtjfup2beH+ppqGptbaWyN09jajq/9ANPYxmSzC79xAdjkVPJ29FRqhs4iOGQMseGjKB0+irKiMOUFLoUmAdaFglLw6zx7kWxQoXZ0cqWPtK7Lih/9C6c0/p3VZ97LzHMXeh1Jcljdvt1seukhSrc8xeTkOwBs8U1gX/nZDPnAAipnnkkwFPY4pUhuOe5CzRhzPvATwAc8YK29o8t4kxm/AGgFrrTWrjjcZ+ZKJyQDSzLlUtUQZ8e+AzRuW05k12uMqn2dyra1+LsciXPM+9f9NidKW6CE+sJJNA47hY6Rc/BXzKSoeAhDC4IURQL4HN3cRORoqVA7OrnSR77+69s4bdvPeb3yJk67/D+9jiN5ZPvbK6l68ymKdv6VKe3r8BuXuA2wJTSVxuFziIyfS/nUuZSNrtSptDKoHVehZozxAZuA84BdwFLgX6216ztNswC4kXShNg/4ibV23uE+N1c6IRkk2ptg7zoSDVU01eymta6K5oSlPhmgrsNPY1sS01ZHoL2OaKKWKfZdKp3qQ7PX2hh7bClVtpSgD4qdODETJ2IS+Az4jcU4Dm3hMppjlcRLJpEcMgkzdAL+IWOIRsIUhvxEgj6iQV/6mrpUEtob09nCRRAu0R0uZcDK90LteHZYHmne7njdR9bs2c7Wx7/F3AN/YFnRR5j9lcf1z7Qcs4a6/Wxdupj2La9RWrucyuQWfJmdpQeIsSdYSXNsArZ0EpGRUykZNZkRFROJRGMeJxfJvuO96+NcYLO1dmvmwx4FLgbWd5rmYuA3Nl31LTHGlBhjRlprq44zu0jfCMVg7HyCQGnmcTjxjhTVNVXE330Dt3otpnE3Q5p2Ud62l6Q1tFBAsx1GtQ2QSEFH0pJKpRjVup+JB9YS29l26LM6rI/ddhgtOCRNBwkSFNBO1LS/Z5kd+GnwDaHBP4zaYAV14TE0RCrAHyHgc/D7HEKmg1iqnsJkPZFUA47jgC+E8Ydww8UkY2NIFY0lWTwWX6QEf8BPwOcQcBz8JAkmDhBor8dn4/jdJD63A18giFM0EmLlEIgcuS2thY5WcFPpdlVxKQNcZoflPXTaYWmMWdR5hyVwATA585gH/ByY18t5c0ZD3X7WP30HM3b8lpkkWVJ2GTO/+CMVaXJciocO55SPXQFcAUBLUz07Nyyl4d0VmOrVFDe9w7TaFymqfSZ9aCCjjiLqfMNpCQ6jPTyMVLQMU1CKv7CUYGw44eJhhAtLKCgaSmHRUELhAq2rMqD0plAbDezs9H4X6U7oSNOMBlSoSV4KB3yUj6yAkRXAJ3s9X3syRVNbB/W1u+nYtwl74F189e/ib9yJcS2tBKmzAdoI0kIBTRTQZEMEOpopSNRSmDzA0OQ+xjW/xdymnr+nyLWGeqIYIEgHIToOXZP3njyZZRksxab1iPkbbJQDFNFgCmkgRsr4idFKlDYKaSVmWyik5dBppCkcWk0BLSZKvTOEBqeEet9Q2k2YAEkCJAnSQcxtJOY2Uug2ELLtpIyfFH5Sxk+zr4RG/1Aa/UNoc2JY42CNHwxEU01EUw0UpuoJu234bBKHJI61tPkKafUX0+IfQtxXSMIXocOJkHRChNw2Iqlmwm4zoVQLoVQrQbeVoBsn4URI+ApI+KK0+6LE/UXE/THafVF8NkXAjeOzCUKpNiLJBsKpRkKpFiw+XOPHdfwkfAW0+YuJ+4uJ+4sOFasGi99tJ5xsJJxsIJxsxrEpDCkcmyLphGg/uDx/jJQTJukESTlB/LaDYLKZUKqZYLIFvxsn4Mbxp9qwxqHDFyXhK6DDV0DCH00/+6IYY/Cn4vjddvxunGAyPX8w1YyxLq4TIOUESJkg7f5CEpllW8cP1sXg4rjJzHKbCSWb8LkJwJLe4W0Ze9mdxEqG9/rvYAA65h2WwPhezNvnNi57ifiBvYfeW+tmni0Gl1QygRtvwU20YNvqCdVtZETLJipsNacBy4vOofzS25lfOS2bMWWQisZKmDr3PJh73qFh1nWp3b+HfdvW0bJ3Kx1123EadxNurSKaqGF029sMqWs4dCSuO0nr0GrCxAnTbsIknBBJEyLphEg6QVwniOtLP1sngPUF09tCJ4B1fOD40w/jgOPDdHqN8aWLwMzNy4xxwBiMcbDGAKbTsPR7jPnnzkxjMAeH4RwcxHtfkJn3nyxOj+OOlTEqZvtKdFgFk085M2uf35tCrbu1outfSW+mwRhzNXA1wNixY3uxaJH8EvL7CMV8EJsI4yce34d1tEH9DkglwFpca+nAT3toKO3+YhLWkEi6dKTc9HNrA/6GHfibdqQLw0QTpqMN09GKa2FHsIRW/xDafEW0O2GS+EkQgGScSHsNBe37ibbvJ9xRT2GygeHJBhybJO5EaXOGs9+Jst0ppNUppMVEcTGEUi1E3CYKkk3E3HpGpvYytX0DIRtPl2kmQAcBmpwYjaaI3b4RxAnhs8l0UUSC4o5GyhNvM809QJS29zRBOwHqTRENFNFEhA78JIngYojRzBC7m0oaidKG8/5NDi2EaSZCKxGabYR6QoRpIkobwzPFZ0GXI5udNdkI9RTSTAQHS4AUAZJEaaOE5sP+w9BiQzRRQBIfSesjhUOhSVBMC4UmfvhfvfXRRohWQsRtEB8uUdNGlDghkzzCipPO3UyEFA7BTMEcJkHEJI44b7MN004Ai8m0qKG1pXmwF2rHs8OyN/MCfdtHtv/ldmbGl/Z6+l2mnH0FU9g5/FKGzbyQ2TPPOK7lixwt4ziUllVQWlbR4zSpZJL6+hqaDuyl5cA+2ptr6WhpINXWgNtWD4kWTKIFp6MFX6oNJ9We2ZEVpyDZit/twG8T+G0Hvsz2PP3aTZ91YlI9LlukO8tj54DHhdouYEyn9xXAnmOYBmvtfcB9kD7//qiSigw2gQgMP+HQWwcIZR7dKwZycwdIr//FtzZ9SqVNgXUJ+cOUGUNZb+braINECyTbIFgIoSKiPj/RI82bbIe2+vS1gv4g+MPgD0EgSsznp8crJFwX2hsg3pBe/kGBAoiUEPWH3rPsztcD21QC29YIyTgk27HJOPgCECqCcDHGF6LAGAp4/x6vjlQC2psh0ZzOjMH6IxAIp5cdLCTk+Ah2U7i2pxIQb0xndpOH9gzj+LGhYgjF8Du+93UMIf+g3/t6PDsse7UjE/q2jyz91I/Z3FL/vojGGDAO/kCQUEGMcEGMSGERFeECev73WCQ3+Px+SoaVUzKsPGvLcFMpUqlk+pHswHVd3FQK66aHW2vBdUm5mdfW4rouWIu1FuumsFiw7qHtvrWk7y5tbXocnfoE+8+zYbreNuI995Gw7z9rptvpjkj/fvelkUXDsvr5vSnUlgKTjTETgN3AQuCzXaZZBNyQOaVjHtCg69NE5KgZAz4/vds0dZkvWJB+HC1/CGJl6cfRcByIDEk/ehWx0//r/hAmdoxHqHxhCIaBY+gc/BEIRaD4KH9WOZ4dlsFezNvnKiadlO1FiAxIjs+H4/MROMxuUZH+csTdpNbaJHAD8GdgA/CYtXadMeYaY8w1mckWA1uBzcD9wHVZyisiItLfDu2wNMYESe+wXNRlmkXA5SZtPv/cYdmbeUVERN6nV7utrbWLSRdjnYfd2+m1Ba7v22giIiLes9YmjTEHd1j6gF8e3GGZGX8v6T5yAekdlq3AFw83rwc/hoiI5JmjPL9IRERk8DmeHZbdzSsiInIkg/4KcRERERERkVyjQk1ERERERCTHqFATERERERHJMSrUREREREREcowKNRERERERkRyjQk1ERERERCTHqFATERERERHJMSb91S8eLNiY/cD24/iIYUBNH8XJtnzKCvmVN5+yQn7lVdbsyae8fZV1nLV2eB98zqBwnH1kPq1fkF958ykr5FfefMoK+ZVXWbOnL/L22D96VqgdL2PMMmvtHK9z9EY+ZYX8yptPWSG/8ipr9uRT3nzKKmn59jvLp7z5lBXyK28+ZYX8yqus2ZPtvDr1UUREREREJMeoUBMREREREckx+Vyo3ed1gKOQT1khv/LmU1bIr7zKmj35lDefskpavv3O8ilvPmWF/MqbT1khv/Iqa/ZkNW/eXqMmIiIiIiIyUOXzETUREREREZEBKacLNWPM+caYt40xm40xt3Uz3hhjfpoZv9oYM8uLnJksY4wxfzPGbDDGrDPG3NzNNGcbYxqMMSszj+94kTWTZZsxZk0mx7JuxudS257Qqc1WGmMajTFf6TKNZ21rjPmlMWafMWZtp2FDjTEvGmPeyTwP6WHew67j/Zj3B8aYjZnf9dPGmJIe5j3setNPWf/DGLO70+96QQ/z5krb/r5T1m3GmJU9zNvfbdvtNiuX1115L/WR2ZMvfWSu94+Z5edNH5lP/eNh8uZkH6n+8RhZa3PyAfiALUAlEARWAdO7TLMA+CNggPnAGx7mHQnMyryOAZu6yXs28Aev2zaTZRsw7DDjc6Ztu1kvqkl/50ROtC1wJjALWNtp2J3AbZnXtwHf7+FnOew63o95Pwr4M6+/313e3qw3/ZT1P4Cv9WI9yYm27TL+LuA7OdK23W6zcnnd1ePofge5tB1XH9lv60RO9Y+Z5edNH5lP/eNh8uZkH6n+8diy5PIRtbnAZmvtVmttAngUuLjLNBcDv7FpS4ASY8zI/g4KYK2tstauyLxuAjYAo73I0kdypm27OBfYYq09ni9L71PW2leAui6DLwYeyrx+CLikm1l7s473ue7yWmtfsNZ//djrAAAD2UlEQVQmM2+XABXZztEbPbRtb+RM2x5kjDHAZ4BHsp2jNw6zzcrZdVfeQ32kt3KmbTvJuf4R8quPzKf+EfKrj1T/eGxyuVAbDezs9H4X79+o92aafmeMGQ+cArzRzejTjDGrjDF/NMac2K/B3ssCLxhjlhtjru5mfE62LbCQnv+Qc6VtAcqstVWQ/oMHRnQzTa628ZdI7ynuzpHWm/5yQ+Y0lF/2cOpBLrbtGcBea+07PYz3rG27bLPyed0dTNRHZlc+9pH50j9C/m5n8qF/hPzrI9U/9iCXCzXTzbCut6jszTT9yhhTCDwJfMVa29hl9ArSpyTMAP4v8Ex/5+vkdGvtLOAC4HpjzJldxudi2waBTwCPdzM6l9q2t3Kxjb8NJIGHe5jkSOtNf/g5MBGYCVSRPl2iq5xrW+BfOfzeQk/a9gjbrB5n62aY1+072KiPzK686iMHYP8IudfG+dA/Qn72keofe5DLhdouYEyn9xXAnmOYpt8YYwKkf6EPW2uf6jreWttorW3OvF4MBIwxw/o55sEsezLP+4CnSR+q7Syn2jbjAmCFtXZv1xG51LYZew+eBpN53tfNNDnVxsaYK4CLgM/ZzInWXfVivck6a+1ea23KWusC9/eQIdfa1g/8C/D7nqbxom172Gbl3bo7SKmPzKI87CPzqX+EPNvO5Ev/mFl+XvWR6h8PL5cLtaXAZGPMhMyeooXAoi7TLAIuN2nzgYaDhyT7W+b82geBDdbau3uYpjwzHcaYuaTbv7b/Uh7KETXGxA6+Jn2h7Nouk+VM23bS4x6XXGnbThYBV2ReXwE82800vVnH+4Ux5nzgG8AnrLWtPUzTm/Um67pcB3JpDxlypm0zPgJstNbu6m6kF217mG1WXq27g5j6yCzJ0z4yn/pHyKPtTD71j5nl51sfqf7xcGw/3p3maB+k76q0ifTdU76dGXYNcE3mtQHuyYxfA8zxMOuHSB/aXA2szDwWdMl7A7CO9B1glgAf9ChrZSbDqkyenG7bTJ4C0h1LcadhOdG2pDvHKqCD9J6Uq4BS4CXgnczz0My0o4DFh1vHPcq7mfQ51QfX3Xu75u1pvfEg628z6+Rq0hu/kbnctpnhvz64rnaa1uu27WmblbPrrh7v+x2qj8xO1rzqI8nh/jGz/LzpI3vImpP942Hy5mQf2V3WzPBfo/6xx4fJfKCIiIiIiIjkiFw+9VFERERERGRQUqEmIiIiIiKSY1SoiYiIiIiI5BgVaiIiIiIiIjlGhZqIiIiIiEiOUaEmIiIiIiKSY1SoiYiIiIiI5BgVaiIiIiIiIjnm/wMeKjTOhmQe9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = np.linspace(0.1,20,100)\n",
    "a = 1     #shape parameter\n",
    "b = 2     #scale parameter\n",
    "c = 9     #shape parameter\n",
    "d = 0.5   #scale parameter\n",
    "\n",
    "lim_ab = 24\n",
    "lim_cd = np.inf\n",
    "cf_gamma_ab = partial(cf_gamma, a=a, b=b)   # function binding \n",
    "cf_gamma_cd = partial(cf_gamma, a=c, b=d)   # function binding \n",
    "\n",
    "fig = plt.figure(figsize=(15,5))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "ax1.plot(xx,ss.gamma.pdf(xx, a, scale=b), label=\"pdf Gamma\")\n",
    "ax1.plot(xx,[Gil_Pelaez_pdf(i,cf_gamma_ab, lim_ab) for i in xx], label=\"Fourier inversion\" )\n",
    "ax1.set_title(\"Comparison Gamma. shape=1, scale=2\"); ax1.legend()\n",
    "ax2.plot(xx,ss.gamma.pdf(xx,c, scale=d), label=\"pdf Gamma\")\n",
    "ax2.plot(xx,[Gil_Pelaez_pdf(i,cf_gamma_cd, lim_cd) for i in xx], label=\"Fourier inversion\" )\n",
    "ax2.set_title(\"Comparison Gamma. shape=9, scale=0.5\"); ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Comments:\n",
    "\n",
    "If you try to increase the value of `lim_ab = 24`, you will see that python will raise:     \n",
    "`IntegrationWarning: The maximum number of subdivisions (50) has been achieved.`\n",
    "\n",
    "When we solve this kind of problems we have to be careful, and analyze them case by case.\n",
    "\n",
    "For $c=9$ and $d=0.5$, we could set `lim_cd = np.inf` because the integrand has a good behavior.    \n",
    "But for $a=1$ and $b=2$ the integrand is not so nice. There are many oscillations (originated by the term $e^{-iux}$) that create the problem.\n",
    "\n",
    "Let's have a look at the plot of the integrands: (at the point x=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = np.linspace(0.1,20,100)\n",
    "x = 3\n",
    "f = lambda u: np.real( np.exp(-u*x*1j) * cf_gamma_ab(u) )  # integrand\n",
    "g = lambda u: np.real( np.exp(-u*x*1j) * cf_gamma_cd(u) )\n",
    "\n",
    "fig = plt.figure(figsize=(15,5)); ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "ax1.plot(u, f(u)); ax1.set_title(\"Integrand: shape=1, scale=2\")\n",
    "ax2.plot(u, g(u)); ax2.set_title(\"Integrand: shape=9, scale=0.5\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Poisson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = np.array(range(20))\n",
    "lam = 4\n",
    "cf_poisson4 = partial(cf_poisson, lam=lam)   # function binding to lam=4\n",
    "\n",
    "fig = plt.figure(figsize=(15,5))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "\n",
    "ax1.plot(k, ss.poisson.pmf(k, 1), linestyle=\"None\", marker='p', label=\"pmf Poisson\")  # with lam=1 \n",
    "ax1.plot(k, [Gil_Pelaez_pdf(i,cf_poisson, np.pi) for i in k], \\\n",
    "         linestyle=\"None\", marker='*', label=\"Fourier inversion\" )      # lam=1 by default\n",
    "ax1.set_xlabel(\"k\"); ax1.set_ylabel(\"P(X=k)\")\n",
    "ax1.set_title(\"Comparison: Poisson pmf - Gil Pelaez, lambda = 1\"); ax1.legend()\n",
    "\n",
    "ax2.plot(k, ss.poisson.pmf(k, lam), linestyle=\"None\", marker='p', label=\"pmf Poisson\")\n",
    "ax2.plot(k, [Gil_Pelaez_pdf(i,cf_poisson4, np.pi) for i in k], \\\n",
    "         linestyle=\"None\", marker='*', label=\"Fourier inversion\" )\n",
    "ax2.set_title(\"Comparison: Poisson pmf - Gil Pelaez, lambda = 4\"); ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Comments:\n",
    "\n",
    "In this case, we considered only the integration in the region $[0,\\pi]$.\n",
    "\n",
    "As you can see in the plots below, the integrand is an even periodic function. Therefore, if we had integrated on $[0,\\infty]$ the integral would have been infinite.\n",
    "\n",
    "The two plots below consider the characteristic function with $\\lambda=1$.     \n",
    "The integrands inside the `Gil_Pelaez_pdf` function are functions of $u$ with fixed values of $x$. For this exaple I chose x=1 and x=10 ($x$ corresponds to $k$ in the plots above).     \n",
    "The characteristic function of a Poisson random variable does not have a damping factor. It is a pure periodic function. For this reason it is helpful to define it only on $[-\\pi,\\pi]$.    \n",
    "The integrand of the Gil Pelaez function simply inherits these features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X1 = 1; X2 = 10\n",
    "y = np.linspace(0.-15,15,2000)\n",
    "ff = lambda u: np.real( np.exp(-u*X1*1j) * cf_poisson(u) )  # integrand\n",
    "gg = lambda u: np.real( np.exp(-u*X2*1j) * cf_poisson(u) )  # integrand\n",
    "\n",
    "fig = plt.figure(figsize=(15,5)); ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "ax1.plot(y, ff(y)); ax1.set_title(\"Integrand at x=1, for lambda = 1\")\n",
    "ax2.plot(y, gg(y)); ax2.set_title(\"Integrand at x=10, for lambda = 1\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3'></a>\n",
    "## Option pricing\n",
    "\n",
    "Let us apply the pricing formula introduced above to the processes:\n",
    "- Geometric Brownian motion\n",
    "- Merton process\n",
    "- Variance Gamma process\n",
    "\n",
    "These processes will be described better in the next notebooks. If you are not familiar with these concepts, have a look at the Appendix **A3**. Otherwise you can skip this part, for now. And come back again after having read the relevant notebooks.\n",
    "\n",
    "First, I have to implement $\\mathbb{Q}$ and $\\tilde{\\mathbb{Q}}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Q1(k, cf, right_lim):\n",
    "    integrand = lambda u: np.real( (np.exp(-u*k*1j) / (u*1j)) * \n",
    "                                  cf(u-1j) / cf(-1j) )  \n",
    "    return 1/2 + 1/np.pi * quad(integrand, 1e-15, right_lim )[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Q2(k, cf, right_lim):\n",
    "    integrand = lambda u: np.real( np.exp(-u*k*1j) /(u*1j) * cf(u) )\n",
    "    return 1/2 + 1/np.pi * quad(integrand, 1e-15, right_lim )[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following, I present European call option values, with the following parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "S0 = 100.0      # spot stock price\n",
    "K = 100.0       # strike \n",
    "T = 1           # maturity\n",
    "k = np.log(K/S0)  # log moneyness"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Geometric Brownian motion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functions.BS_pricer import BS_pricer\n",
    "\n",
    "r = 0.1         # risk free rate  \n",
    "sig = 0.2       # volatility "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fourier inversion call:  13.2696765846609\n",
      "Closed formula call:  13.269676584660893\n"
     ]
    }
   ],
   "source": [
    "cf_GBM = partial(cf_normal, mu=( r - 0.5 * sig**2 )*T, sig=sig*np.sqrt(T))     # function binding\n",
    "call = S0 * Q1(k, cf_GBM, np.inf) - K * np.exp(-r*T) * Q2(k, cf_GBM, np.inf)   # pricing function\n",
    "\n",
    "print(\"Fourier inversion call: \",call)\n",
    "print(\"Closed formula call: \", BS_pricer.BlackScholes(\"call\",S0,K,T,r,sig))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Merton process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# characteristic function of the Merton process at time t\n",
    "\n",
    "def cf_mert(u, t=1, mu=1, sig=2, lam=0.8, muJ=0, sigJ=0.5):\n",
    "    return np.exp( t * ( 1j * u * mu - 0.5 * u**2 * sig**2 \\\n",
    "                  + lam*( np.exp(1j*u*muJ - 0.5 * u**2 * sigJ**2) -1 ) ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This code just creates the object that we use to call the Merton closed formula\n",
    "from functions.Parameters import Option_param\n",
    "from functions.Processes import Merton_process\n",
    "from functions.Merton_pricer import Merton_pricer\n",
    "\n",
    "opt_param = Option_param(S0=100, K=100, T=1, exercise=\"European\", payoff=\"call\" )\n",
    "Merton_param = Merton_process(r=0.1, sig=0.2, lam=0.8, muJ=0, sigJ=0.5)\n",
    "Merton = Merton_pricer(opt_param, Merton_param)\n",
    "\n",
    "r=0.1      # risk free rate \n",
    "sig=0.2    # diffusion coefficient\n",
    "lam=0.8    # jump activity\n",
    "muJ=0      # jump mean size \n",
    "sigJ=0.5   # jump std deviation\n",
    "m = lam * (np.exp(muJ + (sigJ**2)/2) -1)     # martingale correction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fourier inversion call:  22.0163676219057\n",
      "Closed formula call:  22.016367621905697\n"
     ]
    }
   ],
   "source": [
    "# function binding\n",
    "cf_Mert = partial(cf_mert, t=T, mu=( r - 0.5 * sig**2 -m ), sig=sig, lam=lam, muJ=muJ, sigJ=sigJ ) \n",
    "\n",
    "# call price\n",
    "call = S0 * Q1(k, cf_Mert, np.inf) - K * np.exp(-r*T) * Q2(k, cf_Mert, np.inf)   # pricing function\n",
    "\n",
    "print(\"Fourier inversion call: \", call)\n",
    "print(\"Closed formula call: \", Merton.closed_formula() )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance Gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# characteristic function of the VG process at time t, with an additional drift mu\n",
    "\n",
    "def cf_VG(u, t=1, mu=0, theta=-0.1, sigma=0.2, kappa=0.1):\n",
    "    return np.exp( t * ( 1j*mu*u - np.log(1 - 1j*theta*kappa*u + 0.5*kappa*sigma**2 * u**2 ) /kappa  ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# I import some modules in order to call the Monte Carlo pricer\n",
    "from functions.Processes import VG_process\n",
    "from functions.VG_pricer import VG_pricer\n",
    "\n",
    "# Creates the object with the parameters of the process\n",
    "VG_param = VG_process(r=0.1, sigma=0.2, theta=-0.1, kappa=0.1)\n",
    "# Creates the VG process\n",
    "VG = VG_pricer(opt_param, VG_param)\n",
    "\n",
    "theta = -0.1; sigma = 0.2; kappa = 0.1          # VG parameters \n",
    "w = -np.log(1 - theta * kappa - kappa/2 * sigma**2 ) /kappa    # martingale correction w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fourier inversion call:  13.314022\n",
      "Monte Carlo call: 13.311236 with standard error: 0.002252 \n"
     ]
    }
   ],
   "source": [
    "# function binding\n",
    "cf_VG_b = partial(cf_VG, t=T, mu=r-w, theta=theta, sigma=sigma, kappa=kappa ) \n",
    "\n",
    "# call price\n",
    "call = S0 * Q1(k, cf_VG_b, np.inf) - K * np.exp(-r*T) * Q2(k, cf_VG_b, np.inf)   # pricing function\n",
    "\n",
    "print(\"Fourier inversion call: \", call.round(6))\n",
    "print(\"Monte Carlo call: {0:.6f} with standard error: {1:.6f} \".format(*VG.MC(N=50000000, Err=True) ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The closed formula for the VG price is also available, but it is not very reliable (it has a negative bias).  See also the comments in the notebook **3.2**.       \n",
    "For this reason I prefer to compare the Fourier inversion price with the Monte Carlo price!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Martin Schmelze (2010), Option Pricing Formulae using Fourier Transform: Theory and Application. \n",
    "\n",
    "[2] N.G. Shephard (1991), \"From characteristic function to distribution function, a simple framework for the theory\", Econometric Theory, 7, 519-529."
   ]
  }
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